I need to run a ground wire for my inverter - the ground wire will run over a couple of floor joists. Is there a problem with this?

Over, under or through the joist. Over the joist would indicate a truss. It should be protected like any current carrying wire.

Are you referring to an inverter... like a solar system inverter?

And yes, there is a problem with this... all circuit conductors including all neutrals and grounds are required to be run together, with a few specific exceptions.
Now, which ground are we talking about? The equipment ground? Or the grounding electrode conductor? Identifying which ground you are working with is important as they are installed in specific ways in accordance with the electrical code.
Realize that a solar array on a roof can make a lightning strike more probable so the grounding becomes more than just a good idea...